I fitted a replacement extractor fan yesterday and was careful to wire it as the one I was replacing. I works fine other than it seems to be sucking in air rather than extracting it. It has three wires: Permanent Live, Switched Live and Neutral. Any ideas?

Fitted wrong way around. Most single phase motors use either a capacitor or a centrifugal switch to ensure they start in the right direction. It is unlikely that incorrect wiring in the problem. However it is worth switching on a few times and noting if it runs in same direction each time.

I have an ice-cream maker which seems to have a mind of it's own and simply unplugging and re-plugging in will cure it.

There are many different designs used with fans. The fans in your computer are likely 3 phase and a small inverter turns the supply to three phase and drives the squirrel cage motor. Some fans are brushed and can run on AC or DC. Some have capacitor start. And some have a centrifugal switch. In the main swapping the supply wires will not change the direction it is nearly always something inside the fan its self.

In most cases the impeller or fan is curved so in real terms even if you do reverse the rotation it will not work very well in reverse. The leading edge of the blade will be flatter to the case than the output side as the air speeds up as it goes through the fan concave side to direction of rotation. If the fan is designed to work both directions the blades will be flat.